IA Scholar Query: Determining a rotation of a tetrahedron from a projection
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 28 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Homological- and analytical-preserving serendipity framework for polytopal complexes, with application to the DDR method
https://scholar.archive.org/work/fa2jy35znzeajipmki63npwc7i
In this work we investigate from a broad perspective the reduction of degrees of freedom through serendipity techniques for polytopal methods compatible with Hilbert complexes. We first establish an abstract framework that, given two complexes connected by graded maps, identifies a set of properties enabling the transfer of the homological and analytical properties from one complex to the other. This abstract framework is designed having in mind discrete complexes, with one of them being a reduced version of the other, such as occurring when applying serendipity techniques to numerical methods. We then use this framework as an overarching blueprint to design a serendipity DDR complex. Thanks to the combined use of higher-order reconstructions and serendipity, this complex compares favorably in terms of degrees of freedom (DOF) count to all the other polytopal methods previously introduced and also to finite elements on certain element geometries. The gain resulting from such a reduction in the number of DOFs is numerically evaluated on two model problems: a magnetostatic model, and the Stokes equations.Daniele A. Di Pietro, Jérôme Droniouwork_fa2jy35znzeajipmki63npwc7iWed, 28 Sep 2022 00:00:00 GMTSeed-directed synthesis of chiroptically active Au nanocrystals of varied symmetries
https://scholar.archive.org/work/ucxtx6gr5zaw7c343tzbdffdqy
Chiral plasmonic nanocrystals with varied symmetries were synthesized by L-glutathione-guided overgrowth from Au tetrahedra, nanoplates, and octahedra, highlighting the importance of chiral molecule adsorption at transient kink sites. Large g-factors are possible and depend on symmetry. Simulations of their chiroptical properties from tomographically obtained nanocrystal models further verify their chirality.Jack S Googasian, George R Lewis, Zachary J Woessner, Emilie Ringe, Sara E Skrabalakwork_ucxtx6gr5zaw7c343tzbdffdqyWed, 28 Sep 2022 00:00:00 GMTPredicting cell stress and strain during extrusion bioprinting
https://scholar.archive.org/work/7ud7tvna7bhwnoktmrtmyriqh4
Bioprinting of living cells can cause major shape deformations, which may severely affect cell survival and functionality. While the shear stresses occurring during cell flow through the printer nozzle have been quantified to some extent, the extensional stresses occurring as cells leave the nozzle into the free printing strand have been mostly ignored. Here we use Lattice-Boltzmann simulations together with a finite-element based cell model to study cell deformation at the nozzle exit. Our simulation results are in good qualitative agreement with experimental microscopy images. We show that for cells flowing in the center of the nozzle extensional stresses can be significant, while for cells flowing off-center their deformation is dominated by the shear flow inside the nozzle. From the results of these simulations, we develop two simple methods that only require the printing parameters (nozzle diameter, flow rate, bioink rheology) to (i) accurately predict the maximum cell stress occurring during the 3D bioprinting process and (ii) approximately predict the cell strains caused by the elongational flow at the nozzle exit.Sebastian Johannes Mueller, Ben Fabry, Stephan Geklework_7ud7tvna7bhwnoktmrtmyriqh4Wed, 28 Sep 2022 00:00:00 GMTAn Extension of Heron's Formula to Tetrahedra, and the Projective Nature of Its Zeros
https://scholar.archive.org/work/wq4vgu5fmfdtrmsnbtmke6m3kq
A natural extension of Heron's 2000 year old formula for the area of a triangle to the volume of a tetrahedron is presented. This gives the fourth power of the volume as a polynomial in six simple rational functions of the areas of its four faces and three medial parallelograms, which will be referred to herein as "interior faces." Geometrically, these rational functions are the areas of the triangles into which the exterior faces are divided by the points at which the tetrahedron's in-sphere touches those faces. This leads to a conjecture as to how the formula extends to n-dimensional simplices for all n > 3. Remarkably, for n = 3 the zeros of the polynomial constitute a five-dimensional semi-algebraic variety consisting almost entirely of collinear tetrahedra with vertices separated by infinite distances, but with generically well-defined distance ratios. These unconventional Euclidean configurations can be identified with a quotient of the Klein quadric by an action of a group of reflections isomorphic to ℤ_2^4, wherein four-point configurations in the affine plane constitute a distinguished three-dimensional subset. The paper closes by noting that the algebraic structure of the zeros in the affine plane naturally defines the associated 4-element, rank-3 chirotope, aka affine oriented matroid.Timothy F. Havelwork_wq4vgu5fmfdtrmsnbtmke6m3kqWed, 28 Sep 2022 00:00:00 GMTThermal Transport Properties of Diamond Phonons by Electric Field
https://scholar.archive.org/work/eayhmpyscbgstfxjgx6mgyvf4a
For the preparation of diamond heat sinks with ultra-high thermal conductivity by Chemical Vapor Deposition (CVD) technology, the influence of diamond growth direction and electric field on thermal conductivity is worth exploring. In this work, the phonon and thermal transport properties of diamond in three crystal orientation groups (<100>, <110>, and <111>) were investigated using first-principles calculations by electric field. The results show that the response of the diamond in the three-crystal orientation groups presented an obvious anisotropy under positive and negative electric fields. The electric field can break the symmetry of the diamond lattice, causing the electron density around the C atoms to be segregated with the direction of the electric field. Then the phonon spectrum and the thermodynamic properties of diamond were changed. At the same time, due to the coupling relationship between electrons and phonons, the electric field can affect the phonon group velocity, phonon mean free path, phonon–phonon interaction strength and phonon lifetime of the diamond. In the crystal orientation [111], when the electric field strength is ±0.004 a.u., the thermal conductivity is 2654 and 1283 , respectively. The main reason for the change in the thermal conductivity of the diamond lattice caused by the electric field is that the electric field has an acceleration effect on the extranuclear electrons of the C atoms in the diamond. Due to the coupling relationship between the electrons and the phonons, the thermodynamic and phonon properties of the diamond change.Yongsheng Zhao, Fengyun Yan, Xue Liu, Hongfeng Ma, Zhenyu Zhang, Aisheng Jiaowork_eayhmpyscbgstfxjgx6mgyvf4aWed, 28 Sep 2022 00:00:00 GMTPredicting cell stress and strain during extrusion bioprinting
https://scholar.archive.org/work/435awdr25bgpjb42wnx7zlraqu
Bioprinting of living cells can cause major shape deformations, which may severely affect cell survival and functionality. While the shear stresses occurring during cell flow through the printer nozzle have been quantified to some extent, the extensional stresses occurring as cells leave the nozzle into the free printing strand have been mostly ignored. Here we use Lattice-Boltzmann simulations together with a finite-element based cell model to study cell deformation at the nozzle exit. Our simulation results are in good qualitative agreement with experimental microscopy images. We show that for cells flowing in the center of the nozzle extensional stresses can be significant, while for cells flowing off-center their deformation is dominated by the shear flow inside the nozzle. From the results of these simulations, we develop two simple methods that only require the printing parameters (nozzle diameter, flow rate, bioink rheology) to (i) accurately predict the maximum cell stress occurring during the 3D bioprinting process and (ii) approximately predict the cell strains caused by the elongational flow at the nozzle exit.Sebastian Johannes Müller and Ben Fabry and Stephan Geklework_435awdr25bgpjb42wnx7zlraquTue, 27 Sep 2022 00:00:00 GMTTowards Quantum Advantage on Noisy Quantum Computers
https://scholar.archive.org/work/vy7q3xiryfgdregta54odzx6si
Topological data analysis (TDA) is a powerful technique for extracting complex and valuable shape-related summaries of high-dimensional data. However, the computational demands of classical TDA algorithms are exorbitant, and quickly become impractical for high-order characteristics. Quantum computing promises exponential speedup for certain problems. Yet, many existing quantum algorithms with notable asymptotic speedups require a degree of fault tolerance that is currently unavailable. In this paper, we present NISQ-TDA, the first fully implemented end-to-end quantum machine learning algorithm needing only a linear circuit-depth, that is applicable to non-handcrafted high-dimensional classical data, with potential speedup under stringent conditions. The algorithm neither suffers from the data-loading problem nor does it need to store the input data on the quantum computer explicitly. Our approach includes three key innovations: (a) an efficient realization of the full boundary operator as a sum of Pauli operators; (b) a quantum rejection sampling and projection approach to restrict a uniform superposition to the simplices of the desired order in the complex; and (c) a stochastic rank estimation method to estimate the topological features in the form of approximate Betti numbers. We present theoretical results that establish additive error guarantees for NISQ-TDA, and the circuit and computational time and depth complexities for exponentially scaled output estimates, up to the error tolerance. The algorithm was successfully executed on quantum computing devices, as well as on noisy quantum simulators, applied to small datasets. Preliminary empirical results suggest that the algorithm is robust to noise.Ismail Yunus Akhalwaya, Shashanka Ubaru, Kenneth L. Clarkson, Mark S. Squillante, Vishnu Jejjala, Yang-Hui He, Kugendran Naidoo, Vasileios Kalantzis, Lior Horeshwork_vy7q3xiryfgdregta54odzx6siTue, 27 Sep 2022 00:00:00 GMTIt's a Wrap! Visualisations that Wrap Around Cylindrical, Toroidal, or Spherical Topologies
https://scholar.archive.org/work/akpvfdnu2fhgdjsfxa25kjeu2a
Traditional visualisations are designed to be shown on a flat surface (screen or page) but most data is not "flat". For example, the surface of the earth exists on a sphere, however, when that surface is presented on a flat map, key information is hidden, such as geographic paths on the spherical surface being wrapped across the boundaries of the flat map. Similarly, cyclical time-series data has no beginning or end. When such cyclical data is presented on a traditional linear chart, the viewer needs to perceive continuity of the visualisation across the chart's boundaries. Mentally reconnecting the chart across such a boundary may induce additional cognitive load. More complex data such as a network diagram with hundreds or thousands of links between data points leads to a densely connected structure that is even less "flat" and needs to wrap around in multiple dimensions. To improve the usability of these visualisations, this thesis explores a novel class of interactive wrapped data visualisations, i.e., visualisations that wrap around continuously when interactively panned on a two-dimensional projection of surfaces of 3D shapes, specifically, cylinder, torus, or sphere. We start with a systematic exploration of the design space of interactive wrapped visualisations, characterising the visualisations that help people understand the relationship within the data. Subsequently, we investigate a series of wrappable visualisations for cyclical time series, network, and geographic data. We show that these interactive visualisations better preserve the spatial relations in the case of geospatial data, and better reveal the data's underlying structure in the case of abstract data such as networks and cyclical time series. Furthermore, to assist future research and development, we contribute layout algorithms and toolkits to help create pannable wrapped visualisations.Kun-Ting Chenwork_akpvfdnu2fhgdjsfxa25kjeu2aTue, 27 Sep 2022 00:00:00 GMTTaming pseudo-fermion functional renormalization for quantum spins: Finite-temperatures and the Popov-Fedotov trick
https://scholar.archive.org/work/ytqujhmfb5h7rdibb3ejrovibm
The pseudo-fermion representation for S=1/2 quantum spins introduces unphysical states in the Hilbert space which can be projected out using the Popov-Fedotov trick. However, state-of-the-art implementation of the functional renormalization group method for pseudo-fermions have so far omitted the Popov-Fedotov projection. Instead, restrictions to zero temperature were made and absence of unphysical contributions to the ground-state was assumed. We show by numerous counterexamples that this assumption is not generally true. We introduce Popov-Fedotov projection to pseudo-fermion functional renormalization, enabling finite temperature computations with only minor technical modifications to the method. At large and intermediate temperatures, our results are perturbatively controlled and we confirm their accuracy in benchmark calculations. At lower temperatures, the accuracy degrades due to truncation errors in the hierarchy of flow equations. Interestingly, these problems cannot be alleviated by switching to the parquet approximation. We introduce the spin projection as a method-intrinsic quality check. We also show that finite temperature magnetic ordering transitions can be studied via finite-size scaling.Benedikt Schneider, Dominik Kiese, Björn Sbierskiwork_ytqujhmfb5h7rdibb3ejrovibmTue, 27 Sep 2022 00:00:00 GMTKhovanov-Rozansky 𝔰𝔩_N-homology for periodic links
https://scholar.archive.org/work/66fbskniuvcs7fzssf5hbghlza
For an m-periodic link L, we show that the Khovanov-Rozansky 𝔰𝔩_N-homology carries an action of the group ℤ_m. As an example of applications, we prove an analog of the periodicity criterion of Borodzik–Politarczyk using 𝔰𝔩_N-homology instead of Khovanov homology.Maciej Borodzik and Wojciech Politarczyk and Ramazan Yozgyurwork_66fbskniuvcs7fzssf5hbghlzaSat, 24 Sep 2022 00:00:00 GMTClique Homology is QMA1-hard
https://scholar.archive.org/work/xebfmtmnw5hvtfvtnxro7jjnay
We tackle the long-standing question of the computational complexity of determining homology groups of simplicial complexes, a fundamental task in computational topology, posed by Kaibel and Pfetsch 20 years ago. We show that this decision problem is QMA1-hard. Moreover, we show that a version of the problem satisfying a suitable promise and certain constraints is contained in QMA. This suggests that the seemingly classical problem may in fact be quantum mechanical. In fact, we are able to significantly strengthen this by showing that the problem remains QMA1-hard in the case of clique complexes, a family of simplicial complexes specified by a graph which is relevant to the problem of topological data analysis. The proof combines a number of techniques from Hamiltonian complexity and homological algebra. We discuss potential implications for the problem of quantum advantage in topological data analysis.Marcos Crichigno, Tamara Kohlerwork_xebfmtmnw5hvtfvtnxro7jjnayFri, 23 Sep 2022 00:00:00 GMTGET3D: A Generative Model of High Quality 3D Textured Shapes Learned from Images
https://scholar.archive.org/work/4t7u4prjffaalbzudendm2dg4m
As several industries are moving towards modeling massive 3D virtual worlds, the need for content creation tools that can scale in terms of the quantity, quality, and diversity of 3D content is becoming evident. In our work, we aim to train performant 3D generative models that synthesize textured meshes which can be directly consumed by 3D rendering engines, thus immediately usable in downstream applications. Prior works on 3D generative modeling either lack geometric details, are limited in the mesh topology they can produce, typically do not support textures, or utilize neural renderers in the synthesis process, which makes their use in common 3D software non-trivial. In this work, we introduce GET3D, a Generative model that directly generates Explicit Textured 3D meshes with complex topology, rich geometric details, and high-fidelity textures. We bridge recent success in the differentiable surface modeling, differentiable rendering as well as 2D Generative Adversarial Networks to train our model from 2D image collections. GET3D is able to generate high-quality 3D textured meshes, ranging from cars, chairs, animals, motorbikes and human characters to buildings, achieving significant improvements over previous methods.Jun Gao, Tianchang Shen, Zian Wang, Wenzheng Chen, Kangxue Yin, Daiqing Li, Or Litany, Zan Gojcic, Sanja Fidlerwork_4t7u4prjffaalbzudendm2dg4mThu, 22 Sep 2022 00:00:00 GMTMaterials to Be Used in Future Magnetic Confinement Fusion Reactors: A Review
https://scholar.archive.org/work/epgz5loxvzey5npxzv3ruixwja
This paper presents the roadmap of the main materials to be used for ITER and DEMO class reactors as well as an overview of the most relevant innovations that have been made in recent years. The main idea in the EUROfusion development program for the FW (first wall) is the use of low-activation materials. Thus far, several candidates have been proposed: RAFM and ODS steels, SiC/SiC ceramic composites and vanadium alloys. In turn, the most relevant diagnostic systems and PFMs (plasma-facing materials) will be described, all accompanied by the corresponding justification for the selection of the materials as well as their main characteristics. Finally, an outlook will be provided on future material development activities to be carried out during the next phase of the conceptual design for DEMO, which is highly dependent on the success of the IFMIF-DONES facility, whose design, operation and objectives are also described in this paper.René Alba, Roberto Iglesias, María Ángeles Cerdeirawork_epgz5loxvzey5npxzv3ruixwjaThu, 22 Sep 2022 00:00:00 GMTLayered character models for fast physics-based simulation
https://scholar.archive.org/work/e2u77bn53fd65kfxyzs6sycpmq
This thesis presents two different layered character models that are ready to be used in physics-based simulations, in particular they enable convincing character animations in real-time. We start by introducing a two-layered model consisting of rigid bones and an elastic soft tissue layer that is efficiently constructed from a surface mesh of the character and its underlying skeleton. Building on this model, we introduce Fast Projective Skinning, a novel approach for physics-based character skinning. While maintaining real-time performance it overcomes the well-known artifacts of commonly used geometric skinning approaches. It further enables dynamic effects and resolves local and global self-collisions. In particular, our method neither requires skinning weights, which are often expensive to compute or tedious to hand-tune, nor a complex volumetric tessellation, which fails for many real-world input meshes due to self-intersections. By developing a custom-tailored GPU implementation and a high-quality upsampling method, our ap- proach is the first skinning method capable of detecting and handling arbitrary global collisions in real-time. In the second part of the thesis, we extend the idea of a simplified two-layered volumetric model by developing an anatomically plausible three-layered representation of human virtual characters. Starting with an anatomy model of the male and female body, we show how to generate a layered body template for both sexes. It is composed of three surfaces for bones, muscles and skin enclosing the volumetric skeleton, muscles and fat tissues. Utilizing the simple structure of these templates, we show how to fit them to the surface scan of a person in just a few seconds. Our approach includes a data-driven method for estimating the amount of muscle mass and fat mass from a surface scan, which provides more accurate fits to the variety of human body shapes compared to previous approaches. Additionally, we demonstrate how to efficiently embed fine-scale anatomical details, such as high [...]Martin Komaritzan, Technische Universität Dortmundwork_e2u77bn53fd65kfxyzs6sycpmqThu, 22 Sep 2022 00:00:00 GMTEntanglement of inhomogeneous free fermions on hyperplane lattices
https://scholar.archive.org/work/5wy56756dveevavkq2e4e3hsgq
We introduce an inhomogeneous model of free fermions on a (D-1)-dimensional lattice with D(D-1)/2 continuous parameters that control the hopping strength between adjacent sites. We solve this model exactly, and find that the eigenfunctions are given by multidimensional generalizations of Krawtchouk polynomials. We construct a Heun operator that commutes with the chopped correlation matrix, and compute the entanglement entropy numerically for D=2,3,4, for a wide range of parameters. For D=2, we observe oscillations in the sub-leading contribution to the entanglement entropy, for which we conjecture an exact expression. For D>2, we find logarithmic violations of the area law for the entanglement entropy with nontrivial dependence on the parameters.Pierre-Antoine Bernard, Nicolas Crampé, Rafael I. Nepomechie, Gilles Parez, Loïc Poulain d'Andecy, Luc Vinetwork_5wy56756dveevavkq2e4e3hsgqThu, 22 Sep 2022 00:00:00 GMTCommon Mechanism of Activated Catalysis in P-Loop Fold Nucleoside Triphosphatases—United in Diversity
https://scholar.archive.org/work/nae3fb6sq5edhiinde6pw2aqti
To clarify the obscure hydrolysis mechanism of ubiquitous P-loop-fold nucleoside triphosphatases (Walker NTPases), we analysed the structures of 3136 catalytic sites with bound Mg-NTP complexes or their analogues. Our results are presented in two articles; here, in the second of them, we elucidated whether the Walker A and Walker B sequence motifs—common to all P-loop NTPases—could be directly involved in catalysis. We found that the hydrogen bonds (H-bonds) between the strictly conserved, Mg-coordinating Ser/Thr of the Walker A motif ([Ser/Thr]WA) and aspartate of the Walker B motif (AspWB) are particularly short (even as short as 2.4 ångströms) in the structures with bound transition state (TS) analogues. Given that a short H-bond implies parity in the pKa values of the H-bond partners, we suggest that, in response to the interactions of a P-loop NTPase with its cognate activating partner (which are analysed in the first article, reference, Biomolecules-1832854), a proton relocates from [Ser/Thr]WA to AspWB. The resulting anionic [Ser/Thr]WA alkoxide withdraws a proton from the catalytic water molecule, and the nascent hydroxyl attacks the gamma phosphate of NTP. When the gamma-phosphate breaks away, the trapped proton at AspWB passes by the Grotthuss relay via [Ser/Thr]WA to beta-phosphate and compensates for its developing negative charge that is thought to be responsible for the activation barrier of hydrolysis.Maria I. Kozlova, Daria N. Shalaeva, Daria V. Dibrova, Armen Y. Mulkidjanianwork_nae3fb6sq5edhiinde6pw2aqtiThu, 22 Sep 2022 00:00:00 GMTPrethermalization and the local robustness of gapped systems
https://scholar.archive.org/work/gf4dfh2y4bdgxnxug6adljt5g4
We prove that prethermalization is a generic property of gapped local many-body quantum systems, subjected to small perturbations, in any spatial dimension. More precisely, let H_0 be a Hamiltonian, spatially local in d spatial dimensions, with a gap Δ in the many-body spectrum; let V be a spatially local Hamiltonian consisting of a sum of local terms, each of which is bounded by ϵ≪Δ. Then, the approximation that quantum dynamics is restricted to the low-energy subspace of H_0 is accurate, in the correlation functions of local operators, for stretched exponential time scale τ∼exp[(Δ/ϵ)^a] for any a<1/(2d-1). This result does not depend on whether the perturbation closes the gap. It significantly extends previous rigorous results on prethermalization in models where H_0 had an integer-valued spectrum. We infer the robustness of quantum simulation in low-energy subspaces, the existence of "scarring" (strongly athermal correlation functions) in gapped systems subject to generic perturbations, and the robustness of quantum information in non-frustration-free gapped phases with topological order.Chao Yin, Andrew Lucaswork_gf4dfh2y4bdgxnxug6adljt5g4Thu, 22 Sep 2022 00:00:00 GMTSymmetry fractionalization in the gauge mean-field theory of quantum spin ice
https://scholar.archive.org/work/4wkpqb7vazbu5ky5s2i7hq7dyq
Symmetry fractionalization is a ubiquitous feature of topologically ordered states that can be used to classify different symmetry-enriched topological phases and reveal some of their unique experimental signatures. Despite its vast popularity, there is currently no available framework to study symmetry fractionalization of quantum spin ice (QSI) – a U(1) quantum spin liquid (QSL) on the pyrochlore lattice supporting emergent photons – within the most widely used theoretical framework to describe it, gauge mean-field theory (GMFT). In this work, we provide an extension of GMFT that allows for the classification of space-time symmetry fractionalization. The construction classifies all GMFT Ansätze that yield physical wavefunctions invariant under given symmetries and a specific low-energy gauge structure. As an application of the framework, we first show that the only two Ansätze with emergent U(1) gauge fields that respect all space-group symmetries are the well-known 0- and π-flux states. We then showcase how the framework may describe QSLs beyond the currently known ones by classifying chiral U(1) QSI. We find two new states described by π/2- and 3π/2-fluxes of the emergent gauge field threading the hexagonal plaquettes of the pyrochlore lattice. We finally discuss how the different ways translation symmetries fractionalize for all these states lead to unique experimentally relevant signatures and compute their respective inelastic neutron scattering cross-section to illustrate the argument.Félix Desrochers, Li Ern Chern, Yong Baek Kimwork_4wkpqb7vazbu5ky5s2i7hq7dyqThu, 22 Sep 2022 00:00:00 GMTCalcium Orthophosphate (CaPO4)-Based Bioceramics: Preparation, Properties, and Applications
https://scholar.archive.org/work/unlco7bchja7nod7cb2xploze4
Various types of materials have been traditionally used to restore damaged bones. In the late 1960s, a strong interest was raised in studying ceramics as potential bone grafts due to their biomechanical properties. A short time later, such synthetic biomaterials were called bioceramics. Bioceramics can be prepared from diverse inorganic substances, but this review is limited to calcium orthophosphate (CaPO4)-based formulations only, due to its chemical similarity to mammalian bones and teeth. During the past 50 years, there have been a number of important achievements in this field. Namely, after the initial development of bioceramics that was just tolerated in the physiological environment, an emphasis was shifted towards the formulations able to form direct chemical bonds with the adjacent bones. Afterwards, by the structural and compositional controls, it became possible to choose whether the CaPO4-based implants would remain biologically stable once incorporated into the skeletal structure or whether they would be resorbed over time. At the turn of the millennium, a new concept of regenerative bioceramics was developed, and such formulations became an integrated part of the tissue engineering approach. Now, CaPO4-based scaffolds are designed to induce bone formation and vascularization. These scaffolds are usually porous and harbor various biomolecules and/or cells. Therefore, current biomedical applications of CaPO4-based bioceramics include artificial bone grafts, bone augmentations, maxillofacial reconstruction, spinal fusion, and periodontal disease repairs, as well as bone fillers after tumor surgery. Prospective future applications comprise drug delivery and tissue engineering purposes because CaPO4 appear to be promising carriers of growth factors, bioactive peptides, and various types of cells.Sergey V. Dorozhkinwork_unlco7bchja7nod7cb2xploze4Wed, 21 Sep 2022 00:00:00 GMTToy Models of Superposition
https://scholar.archive.org/work/7smxlngtrvfothbkv27ptjq7zq
Neural networks often pack many unrelated concepts into a single neuron - a puzzling phenomenon known as 'polysemanticity' which makes interpretability much more challenging. This paper provides a toy model where polysemanticity can be fully understood, arising as a result of models storing additional sparse features in "superposition." We demonstrate the existence of a phase change, a surprising connection to the geometry of uniform polytopes, and evidence of a link to adversarial examples. We also discuss potential implications for mechanistic interpretability.Nelson Elhage, Tristan Hume, Catherine Olsson, Nicholas Schiefer, Tom Henighan, Shauna Kravec, Zac Hatfield-Dodds, Robert Lasenby, Dawn Drain, Carol Chen, Roger Grosse, Sam McCandlish, Jared Kaplan, Dario Amodei, Martin Wattenberg, Christopher Olahwork_7smxlngtrvfothbkv27ptjq7zqWed, 21 Sep 2022 00:00:00 GMT