Search

We use dualities of quiver moduli induced by reflection functors to describe generating series of motives of Kronecker moduli spaces of central slope as solutions of algebraic and q-difference equations., Comment: 13 pages

We review several algebraic, combinatorial and geometric interpretations of motivic Donaldson-Thomas invariants of symmetric quivers., Comment: Survey written for the Proceedings of the Simons Semester "Knots, homologies and physics"

Light-harvesting devices made from PbS quantum dot (QD) absorbers are one of the many promising technologies of third-generation photovoltaics. Their simple, solution-based fabrication together with a highly tunable and broad light absorption makes their application in newly developed solar cells particularly promising. In order to yield devices with reduced voltage and current losses, PbS QDs need to have strategically passivated surfaces, most commonly achieved through lead iodide and bromide passivation. The interdot spacing is then predominantly filled with residual amorphous lead halide species that remain from the ligand exchange, thus hindering efficient charge transport and reducing device stability. Herein, we demonstrate that a post-treatment by iodide based 2-phenylethlyammonium salts (X-PEAI) and intermediate 2D perovskite formation can be used to manage the lead halide excess in the PbS QD active layer. This treatment results in improved device performance and increased shelf-life stability, demonstrating the importance of interdot spacing management in PbS quantum dot photovoltaics.

Metal oxide (MO) semiconductors are widely used in electronic devices due to their high optical transmittance and promising electrical performance. This work describes the advancement toward an eco-friendly, streamlined method for preparing thin-film transistors (TFTs) via a pure water-solution blade-coating process with focus on a low thermal budget. Low temperature and rapid annealing of triple-coated indium oxide thin-film transistors (3C-TFTs) and indium oxide/zinc oxide/indium oxide thin-film transistors (IZI-TFTs) on a 300 nm SiO2 gate dielectric at 300 $^{\circ}$C for only 60 s yields devices with an average field effect mobility of 10.7 and 13.8 cm2/Vs, respectively. The devices show an excellent on/off ratio (>10^6), and a threshold voltage close to 0 V when measured in air. Flexible MO-TFTs on polyimide substrates with AlOx dielectrics fabricated by rapid annealing treatment can achieve a remarkable mobility of over 10 cm2/Vs at low operating voltage. When using a longer post-coating annealing period of 20 min, high-performance 3C-TFTs (over 18 cm2/Vs) and IZI-TFTs (over 38 cm2/Vs) using MO semiconductor layers annealed at 300 $^{\circ}$C are achieved.

In earlier work of three of the authors of the present paper, a supercommutative quadratic algebra was associated to each symmetric quiver, and a new proof of positivity of motivic Donaldson-Thomas invariants of symmetric quivers was given using the so called numerical Koszul property of these algebras. It was furthermore conjectured that for each symmetric quiver such an algebra is Koszul. In this work, we lift the linking and unlinking operations on symmetric quivers of Ekholm, Longhi and the third author to the level of quadratic algebras, and use those lifts to prove the Koszulness conjecture., Comment: 11 pages, comments are welcome

We introduce a double framing construction for moduli spaces of quiver representations. It allows us to reduce certain sheaf cohomology computations involving the universal representation, to computations involving line bundles, making them amenable to methods from geometric invariant theory. We will use this to show that in many good situations the vector fields on the moduli space are isomorphic as a vector space to the first Hochschild cohomology of the path algebra. We also show that considering the universal representation as a Fourier-Mukai kernel in the appropriate sense gives an admissible embedding of derived categories., Comment: v2: added references, 23 pages, all comments welcome

We explain how Teleman quantization can be applied to moduli spaces of quiver representations to compute the higher cohomology of the endomorphism bundle of the universal bundle. We use this to prove Schofield's partial tilting conjecture, and to show that moduli spaces of quiver representations are (infinitesimally) rigid as varieties., Comment: v2: added references, 26 pages, comments welcome

We verify the Mukai conjecture for Fano quiver moduli spaces associated to dimension vectors in the interior of the fundamental domain., Comment: 4 pages

Basic-block throughput models such as uiCA, IACA, GRANITE, Ithemal, llvm-mca, OSACA, or CQA guide optimizing compilers and help performance engineers identify and eliminate bottlenecks. For this purpose, basic-block throughput models should ideally be fast, accurate, and interpretable. Recent advances have significantly improved accuracy: uiCA, the state-of-the-art model, achieves an error of about 1% relative to measurements across a wide range of microarchitectures. The computational efficiency of throughput models, which is equally important for widespread adoption, especially in compilers, has so far received little attention. In this paper, we introduce Facile, an analytical throughput model that is fast, accurate, and interpretable. Facile analyzes different potential bottlenecks independently and analytically. Due to its compositional nature, Facile's predictions directly pinpoint the bottlenecks. We evaluate Facile on a wide range of microarchitectures and show that it is almost two orders of magnitude faster than existing models while achieving state-of-the-art accuracy.

While instruction cache analysis is essentially a solved problem, data cache analysis is more challenging. In contrast to instruction fetches, the data accesses generated by a memory instruction may vary with the program's inputs and across dynamic occurrences of the same instruction in loops. We observe that the plain control-flow graph (CFG) abstraction employed in classical cache analyses is inadequate to capture the dynamic behavior of memory instructions. On top of plain CFGs, accurate analysis of the underlying program's cache behavior is impossible. Thus, our first contribution is the definition of a more expressive program abstraction coined symbolic control-flow graphs, which can be obtained from LLVM's ScalarEvolution analysis. To exploit this richer abstraction, our main contribution is the development of symbolic data cache analysis, a smooth generalization of classical LRU must analysis from plain to symbolic control-flow graphs. The experimental evaluation demonstrates that symbolic data cache analysis consistently outperforms classical LRU must analysis both in terms of accuracy and analysis runtime., Comment: Extended version of RTSS 2023 paper including definitions and proofs omitted in the conference version due to space constraints

We use cluster algebras to interpret Floer potentials of monotone Lagrangian tori in toric del Pezzo surfaces as cluster characters of quiver representations., Comment: 14 pages

Leakage contracts have recently been proposed as a new security abstraction at the Instruction Set Architecture (ISA) level. Such contracts aim to faithfully capture the information processors may leak through side effects of their microarchitectural implementations. However, so far, we lack a verification methodology to check that a processor actually satisfies a given leakage contract. In this paper, we address this problem by developing LeaVe, the first tool for verifying register-transfer-level (RTL) processor designs against ISA-level leakage contracts. To this end, we introduce a decoupling theorem that separates security and functional correctness concerns when verifying contract satisfaction. LeaVe leverages this decoupling to make verification of contract satisfaction practical. To scale to realistic processor designs LeaVe further employs inductive reasoning on relational abstractions. Using LeaVe, we precisely characterize the side-channel security guarantees provided by three open-source RISC-V processors, thereby obtaining the first contract satisfaction proofs for RTL processor designs., Comment: Technical report containing full formalization and proofs of all results. A short version of this report (with the same title) appears in the proceedings of the 30th ACM SIGSAC Conference on Computer and Communication Security (CCS 2023)

The energetic landscape at the interface between electron donating and accepting molecular materials favors efficient conversion of intermolecular charge-transfer states (CTS) into free charge carriers in high-performance organic solar cells. Here, we elucidate how interfacial energetics, charge generation and radiative recombination are affected by structural ordering. We experimentally determine the CTS binding energy of a series of model, small molecule donor-acceptor blends, where the used acceptors (B2PYMPM, B3PYMPM and B4PYMPM) differ only in the nitrogen position of their lateral pyridine rings. We find that the formation of an ordered, face-on molecular packing in B4PYMPM is beneficial to efficient, field-independent charge separation, leading to fill factors over 70% in photovoltaic devices. This is rationalized by a comprehensive computational protocol showing that, compared to the more amorphous and isotropically oriented B2PYMPM, the higher order of the B4PYMPM molecules provides more delocalized CTS. Furthermore, we find no correlation between the quantum efficiency of radiative free charge carrier recombination and the bound or unbound nature of the CTS. This work highlights the importance of structural ordering at donor-acceptor interfaces for efficient free carrier generation and shows that more ordering and less bound CT states do not preclude efficient radiative recombination.

We exhibit and discuss "wild" analogues of the five-term quantum dilogarithm identity. We derive these from the representation theory of quivers, using motivic wall-crossing, the geometricity of motivic Donaldson-Thomas invariants, and special properties of Kronecker moduli, Comment: 7 pages

We construct torus equivariant desingularizations of quiver Grassmannians for arbitrary nilpotent representations of an equioriented cycle quiver. We apply this to the computation of their torus equivariant cohomology., Comment: 20 pages

We apply the method of orbit harmonics to the set of break divisors and orientable divisors on graphs to obtain the central and external zonotopal algebras respectively. We then relate a construction of Efimov in the context of cohomological Hall algebras to the central zonotopal algebra of a graph $G_{Q,\gamma}$ constructed from a symmetric quiver $Q$ with enough loops and a dimension vector $\gamma$. This provides a concrete combinatorial perspective on the former work, allowing us to identify the quantum Donaldson-Thomas invariants as the Hilbert series of the space of $S_{\gamma}$-invariants of the Postnikov-Shapiro slim subgraph space attached to $G_{Q,\gamma}$. The connection with orbit harmonics in turn allows us to give a manifestly nonnegative combinatorial interpretation to numerical Donaldson-Thomas invariants as the number of $S_{\gamma}$-orbits under the permutation action on the set of break divisors on $G_{Q,\gamma}$. We conclude with several representation-theoretic consequences, whose combinatorial ramifications may be of independent interest., Comment: minor typos corrected

We study moduli spaces of (semi-)stable representations of one-point extensions of quivers by rigid representations. This class of moduli spaces unifies Grassmannians of subrepresentations of rigid representations and moduli spaces of representations of generalized Kronecker quivers. With homological methods, we find numerical criteria for non-emptiness and results on basic geometric properties, construct generating semi-invariants, expand the Gel'fand MacPherson correspondence, and derive a formula for the Poincare polynomial in singular cohomology of these moduli spaces., Comment: 25 pages

Wavelength discriminating systems typically consist of heavy benchtop-based instruments, comprising diffractive optics, moving parts, and adjacent detectors. For simple wavelengths measurements, such as lab-on-chip light source calibration or laser wavelength tracking, which do not require polychromatic analysis and cannot handle bulky spectroscopy instruments, light-weight, easy-to-process, and flexible single-pixel devices are attracting increasing attention. Here, we propose a device for wavelength tracking with room-temperature phosphorescence at the heart of its functionality that demonstrates a resolution down to one nanometer and below. It is solution-processed from a single host-guest system comprising organic room-temperature phosphors and colloidal quantum dots. The share of excited triplet states within the photoluminescent layer is dependent on the excitation wavelength and determines the afterglow intensity of the film, which is tracked by a simple photodetector. Finally, an all-organic thin-film wavelength sensor and two applications are demonstrated where our novel measurement concept successfully replaces a full spectrometer.

Charge injection from electrodes into doped organic films is a widespread technology used in the majority of state-of-the-art organic semiconductor devices. Although such interfaces are commonly considered to form Ohmic contacts via strong band bending, an experiment that directly measures the contact resistance has not yet been demonstrated. In this study, we use a simple metal/doped organic semiconductor/metal stack and study its voltage-dependent resistance. A transport layer thickness variation proves that the presented experiment gains direct access to the contact resistance of the device. We can quantify that for an operating current density of 10mA/cm2 the investigated material system exhibits a voltage drop over the metal/organic interface of about 200mV, which can be reduced by more than one order of magnitude when employing an additional injection layer. The presented experiment proposes a simple strategy to measure the contact resistance between any metal and doped organic film without applying numerical tools or elaborate techniques. Furthermore, the simplistic device architecture allows for very high, homogeneous, and tunable electric fields within the organic layer, which enables a clear investigation of the Poole-Frenkel effect.

Techniques to evaluate a program's cache performance fall into two camps: 1. Traditional trace-based cache simulators precisely account for sophisticated real-world cache models and support arbitrary workloads, but their runtime is proportional to the number of memory accesses performed by the program under analysis. 2. Relying on implicit workload characterizations such as the polyhedral model, analytical approaches often achieve problem-size-independent runtimes, but so far have been limited to idealized cache models. We introduce a hybrid approach, warping cache simulation, that aims to achieve applicability to real-world cache models and problem-size-independent runtimes. As prior analytical approaches, we focus on programs in the polyhedral model, which allows to reason about the sequence of memory accesses analytically. Combining this analytical reasoning with information about the cache behavior obtained from explicit cache simulation allows us to soundly fast-forward the simulation. By this process of warping, we accelerate the simulation so that its cost is often independent of the number of memory accesses., Comment: Extended version of PLDI 2022 paper

Metasurfaces have appeared as a versatile platform for miniaturized functional nonlinear optics due to their design freedom in tailoring wavefronts. The key factor that limits its application in functional devices is the low conversion efficiency. Recently, dielectric metasurfaces governed by either high-quality factor modes (quasi-bound states in the continuum) or Mie modes, enabling strong light-matter interaction, have become a prolific route to achieve high nonlinear efficiency. Here, we demonstrate both numerically and experimentally an effective way of spatial nonlinear phase control by using the Pancharatnam-Berry phase principle with a high third harmonic conversion efficiency of $10^{-4}$ $1/W^2$. We find that the magnetic Mie resonance appears to be the main contributor to the third harmonic response, while the contribution from the quasi-bound states in the continuum is negligible. This is confirmed by a phenomenological model based on coupled anharmonic oscillators. Besides, our metasurface provides experimentally a high diffraction efficiency (80-90%) in both polarization channels. We show a functional application of our approach by experimentally reconstructing an encoded polarization-multiplexed vortex beam array with different topological charges at the third harmonic frequency with high fidelity. Our approach has the potential viability for future on-chip nonlinear signal processing and wavefront control.

We relate the notion of dimension expanders to quiver representations and their general subrepresentations, and use this relation to establish sharp existence results., Comment: 6 pages

For a given symmetric quiver $Q$, we define a supercommutative quadratic algebra $\mathcal{A}_Q$ whose Poincar\'e series is related to the motivic generating function of $Q$ by a simple change of variables. The Koszul duality between supercommutative algebras and Lie superalgebras assigns to the algebra $\mathcal{A}_Q$ its Koszul dual Lie superalgebra $\mathfrak{g}_Q$. We prove that the motivic Donaldson-Thomas invariants of the quiver $Q$ may be computed using the Poincar\'e series of a certain Lie subalgebra of $\mathfrak{g}_Q$ that can be described, using an action of the first Weyl algebra on $\mathfrak{g}_Q$, as the kernel of the operator $\partial_t$. This gives a new proof of positivity for motivic Donaldson--Thomas invariants. In addition, we prove that the algebra $\mathcal{A}_Q$ is numerically Koszul for every symmetric quiver $Q$ and conjecture that it is in fact Koszul; we also prove this conjecture for quivers of a certain class., Comment: 25 pages, the main result on DT invariants of symmetric quivers is now not conditional on Koszulness

We study the action of $S_n$ on the set of break divisors on complete multigraphs $K_{n}^m$. We provide an alternative characterization for these divisors, by virtue of which we show that orbits of this action are enumerated by the numerical Donaldson-Thomas invariants of $(m+1)$-loop quivers. Our characterization also allows us to restrict this action to $S_{n-1}$ and we identify the resulting $S_{n-1}$-module as that afforded by $K_n^m$-parking functions.