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In 1967, Katona and Szemer\'{e}di showed that no undirected graph with $n$ vertices and fewer than $\frac{n}{2}\log_2\frac{n}{2}$ edges admits an orientation of diameter two. In 1978, Chv\'atal and Thomassen revealed the complexity of determining whether an undirected graph can be oriented to achieve a diameter of two, proving it to be NP-complete. This breakthrough has sparked ongoing interest in identifying sufficient conditions for graphs to be oriented with the smallest possible diameter of two -- critical for optimizing communication and network flow in larger structures. In 2019, Czabarka, Dankelmann, and Sz\'ekely significantly advanced this field by establishing that the minimum degree threshold for achieving such an orientation in undirected graphs of order $n$ is $\frac{n}{2} + \Theta(\ln n)$. In this paper, we extend this foundational result by determining the minimum degree threshold necessary for realizing an orientation with diameter two in mixed graphs, which contain both undirected and directed edges. Mixed graphs offer a versatile framework, representing an intermediate stage in the orientation process, making our findings a substantial generalization of previous results.

Understanding how biological visual systems process information is challenging because of the nonlinear relationship between visual input and neuronal responses. Artificial neural networks allow computational neuroscientists to create predictive models that connect biological and machine vision. Machine learning has benefited tremendously from benchmarks that compare different model on the same task under standardized conditions. However, there was no standardized benchmark to identify state-of-the-art dynamic models of the mouse visual system. To address this gap, we established the Sensorium 2023 Benchmark Competition with dynamic input, featuring a new large-scale dataset from the primary visual cortex of ten mice. This dataset includes responses from 78,853 neurons to 2 hours of dynamic stimuli per neuron, together with the behavioral measurements such as running speed, pupil dilation, and eye movements. The competition ranked models in two tracks based on predictive performance for neuronal responses on a held-out test set: one focusing on predicting in-domain natural stimuli and another on out-of-distribution (OOD) stimuli to assess model generalization. As part of the NeurIPS 2023 competition track, we received more than 160 model submissions from 22 teams. Several new architectures for predictive models were proposed, and the winning teams improved the previous state-of-the-art model by 50%. Access to the dataset as well as the benchmarking infrastructure will remain online at www.sensorium-competition.net.

For a positive integer $r$, let $f(r)$ denote the smallest number such that any 2-edge connected mixed graph with radius $r$ has an oriented radius of at most $f(r)$. Recently, Babu, Benson, and Rajendraprasad significantly improved the upper bound of $f(r)$ by establishing that $f(r) \leq 1.5r^2 + r + 1$, see [Improved bounds for the oriented radius of mixed multigraphs, J. Graph Theory, 103 (2023), 674-689]. Additionally, they demonstrated that if each edge of a graph $G$ is contained within a cycle of length at most $\eta$, then the oriented radius of $G$ is at most $1.5r\eta$. The authors' results were derived through Observation 1, which served as the foundation for the development of Algorithm ORIENTOUT and Algorithm ORIENTIN. By integrating these algorithms, they obtained the improved bounds. However, an error has been identified in Observation 1, necessitating revisions to Algorithm ORIENTOUT and Algorithm ORIENTIN. In this note, we address the error and propose the necessary modifications to both algorithms, thereby ensuring the correctness of the conclusions., Comment: 7 pages, 1 figure

Identifying cell types and understanding their functional properties is crucial for unraveling the mechanisms underlying perception and cognition. In the retina, functional types can be identified by carefully selected stimuli, but this requires expert domain knowledge and biases the procedure towards previously known cell types. In the visual cortex, it is still unknown what functional types exist and how to identify them. Thus, for unbiased identification of the functional cell types in retina and visual cortex, new approaches are needed. Here we propose an optimization-based clustering approach using deep predictive models to obtain functional clusters of neurons using Most Discriminative Stimuli (MDS). Our approach alternates between stimulus optimization with cluster reassignment akin to an expectation-maximization algorithm. The algorithm recovers functional clusters in mouse retina, marmoset retina and macaque visual area V4. This demonstrates that our approach can successfully find discriminative stimuli across species, stages of the visual system and recording techniques. The resulting most discriminative stimuli can be used to assign functional cell types fast and on the fly, without the need to train complex predictive models or show a large natural scene dataset, paving the way for experiments that were previously limited by experimental time. Crucially, MDS are interpretable: they visualize the distinctive stimulus patterns that most unambiguously identify a specific type of neuron.

Understanding how biological visual systems process information is challenging due to the complex nonlinear relationship between neuronal responses and high-dimensional visual input. Artificial neural networks have already improved our understanding of this system by allowing computational neuroscientists to create predictive models and bridge biological and machine vision. During the Sensorium 2022, we introduced benchmarks for vision models with static input. However, animals operate and excel in dynamic environments, making it crucial to study and understand how the brain functions under these conditions. Moreover, many biological theories, such as predictive coding, suggest that previous input is crucial for current input processing. Currently, there is no standardized benchmark to identify state-of-the-art dynamic models of the mouse visual system. To address this gap, we propose the Sensorium 2023 Benchmark Competition with dynamic input. It includes the collection of a new large-scale dataset from the primary visual cortex of ten mice, containing responses from over 78,000 neurons to over 2 hours of dynamic stimuli per neuron. Participants in the main benchmark track will compete to identify the best predictive models of neuronal responses for dynamic input. We will also host a bonus track in which submission performance will be evaluated on out-of-domain input, using withheld neuronal responses to dynamic input stimuli whose statistics differ from the training set. Both tracks will offer behavioral data along with video stimuli. As before, we will provide code, tutorials, and strong pre-trained baseline models to encourage participation. We hope this competition will continue to strengthen the accompanying Sensorium benchmarks collection as a standard tool to measure progress in large-scale neural system identification models of the entire mouse visual hierarchy and beyond., Comment: arXiv admin note: substantial text overlap with arXiv:2206.08666

Visual search is a ubiquitous challenge in natural vision, including daily tasks such as finding a friend in a crowd or searching for a car in a parking lot. Human rely heavily on relevant target features to perform goal-directed visual search. Meanwhile, context is of critical importance for locating a target object in complex scenes as it helps narrow down the search area and makes the search process more efficient. However, few works have combined both target and context information in visual search computational models. Here we propose a zero-shot deep learning architecture, TCT (Target and Context-aware Transformer), that modulates self attention in the Vision Transformer with target and contextual relevant information to enable human-like zero-shot visual search performance. Target modulation is computed as patch-wise local relevance between the target and search images, whereas contextual modulation is applied in a global fashion. We conduct visual search experiments on TCT and other competitive visual search models on three natural scene datasets with varying levels of difficulty. TCT demonstrates human-like performance in terms of search efficiency and beats the SOTA models in challenging visual search tasks. Importantly, TCT generalizes well across datasets with novel objects without retraining or fine-tuning. Furthermore, we also introduce a new dataset to benchmark models for invariant visual search under incongruent contexts. TCT manages to search flexibly via target and context modulation, even under incongruent contexts.

The neural underpinning of the biological visual system is challenging to study experimentally, in particular as the neuronal activity becomes increasingly nonlinear with respect to visual input. Artificial neural networks (ANNs) can serve a variety of goals for improving our understanding of this complex system, not only serving as predictive digital twins of sensory cortex for novel hypothesis generation in silico, but also incorporating bio-inspired architectural motifs to progressively bridge the gap between biological and machine vision. The mouse has recently emerged as a popular model system to study visual information processing, but no standardized large-scale benchmark to identify state-of-the-art models of the mouse visual system has been established. To fill this gap, we propose the Sensorium benchmark competition. We collected a large-scale dataset from mouse primary visual cortex containing the responses of more than 28,000 neurons across seven mice stimulated with thousands of natural images, together with simultaneous behavioral measurements that include running speed, pupil dilation, and eye movements. The benchmark challenge will rank models based on predictive performance for neuronal responses on a held-out test set, and includes two tracks for model input limited to either stimulus only (Sensorium) or stimulus plus behavior (Sensorium+). We provide a starting kit to lower the barrier for entry, including tutorials, pre-trained baseline models, and APIs with one line commands for data loading and submission. We would like to see this as a starting point for regular challenges and data releases, and as a standard tool for measuring progress in large-scale neural system identification models of the mouse visual system and beyond., Comment: NeurIPS 2022 Competition Track

Machine learning has demonstrated great power in materials design, discovery, and property prediction. However, despite the success of machine learning in predicting discrete properties, challenges remain for continuous property prediction. The challenge is aggravated in crystalline solids due to crystallographic symmetry considerations and data scarcity. Here we demonstrate the direct prediction of phonon density of states using only atomic species and positions as input. We apply Euclidean neural networks, which by construction are equivariant to 3D rotations, translations, and inversion and thereby capture full crystal symmetry, and achieve high-quality prediction using a small training set of $\sim 10^{3}$ examples with over 64 atom types. Our predictive model reproduces key features of experimental data and even generalizes to materials with unseen elements,and is naturally suited to efficiently predict alloy systems without additional computational cost. We demonstrate the potential of our network by predicting a broad number of high phononic specific heat capacity materials. Our work indicates an efficient approach to explore materials' phonon structure, and can further enable rapid screening for high-performance thermal storage materials and phonon-mediated superconductors., Comment: 21 pages total, 5 main figures + 16 supplementary figures. To appear in Advanced Science (2021)

The electron-phonon interaction (EPI) is instrumental in a wide variety of phenomena in solid-state physics, such as electrical resistivity in metals, carrier mobility, optical transition and polaron effects in semiconductors, lifetime of hot carriers, transition temperature in BCS superconductors, and even spin relaxation in diamond nitrogen-vacancy centers for quantum information processing. However, due to the weak EPI strength, most phenomena have focused on electronic properties rather than on phonon properties. One prominent exception is the Kohn anomaly, where phonon softening can emerge when the phonon wavevector nests the Fermi surface of metals. Here we report a new class of Kohn anomaly in a topological Weyl semimetal (WSM), predicted by field-theoretical calculations, and experimentally observed through inelastic x-ray and neutron scattering on WSM tantalum phosphide (TaP). Compared to the conventional Kohn anomaly, the Fermi surface in a WSM exhibits multiple topological singularities of Weyl nodes, leading to a distinct nesting condition with chiral selection, a power-law divergence, and non-negligible dynamical effects. Our work brings the concept of Kohn anomaly into WSMs and sheds light on elucidating the EPI mechanism in emergent topological materials., Comment: 30 pages, 4 main figures, 11 supplementary figures and 1 theoretical derivation. Feedback most welcome

Thermoelectrics are promising by directly generating electricity from waste heat. However, (sub-)room-temperature thermoelectrics have been a long-standing challenge due to vanishing electronic entropy at low temperatures. Topological materials offer a new avenue for energy harvesting applications. Recent theories predicted that topological semimetals at the quantum limit can lead to a large, non-saturating thermopower and a quantized thermoelectric Hall conductivity approaching a universal value. Here, we experimentally demonstrate the non-saturating thermopower and quantized thermoelectric Hall effect in the topological Weyl semimetal (WSM) tantalum phosphide (TaP). An ultrahigh longitudinal thermopower Sxx= 1.1x10^3 muV/K and giant power factor ~525 muW/cm/K^2 are observed at ~40K, which is largely attributed to the quantized thermoelectric Hall effect. Our work highlights the unique quantized thermoelectric Hall effect realized in a WSM toward low-temperature energy harvesting applications., Comment: 54 pages total, 5 main figures + 22 supplementary figures. To appear in Nature Communications (2020)

Wavelike thermal transport in solids, referred to as second sound, has until now been an exotic phenomenon limited to a handful of materials at low temperatures. This has restricted interest in its occurrence and in its potential applications. Through time-resolved optical measurements of thermal transport on 5-20 {\mu}m length scales in graphite, we have made direct observations of second sound at temperatures above 100 K. The results are in qualitative agreement with ab initio calculations that predict wavelike phonon hydrodynamics on ~ 1-{\mu}m length scale up to almost room temperature. The results suggest an important role of second sound in microscale transient heat transport in two-dimensional and layered materials in a wide temperature range.

We show that a quantum phase transition can occur in a phonon system in the presence of dislocations. Due to the competing nature between the topological protection of the dislocation and anharmonicity, phonons can reach a quantum critical point at a frequency determined by dislocation density and the anharmonic constant, at zero temperature. In the symmetry-broken phase, a novel phonon state is developed with a dynamically-induced dipole field. We carry out a renormalization group analysis and show that the phonon critical behavior differs wildly from any electronic system. In particular, at the critical point, a single phonon mode dominates the density of states and develops an exotic logarithmic divergence in thermal conductivity. This phonon quantum criticality provides a completely new avenue to tailor phonon transport at the single-mode level without using phononic crystals., Comment: 5 pages, 3 figures. Comments and suggestions are most welcome

Through first-principles calculations, the phonon-limited transport properties of cubic boron-V compounds (BP, BAs and BSb) are studied. We find that the high optical phonon frequency in these compounds leads to the substantial suppression of polar scattering and the reduction of inter-valley transition mediated by large-wavevector optical phonons, both of which significantly facilitate charge transport. We also discover that BAs simultaneously has a high hole mobility (2110 cm2/V-s) and electron mobility (1400 cm2/V-s) at room temperature, which is rare in semiconductors. Our findings present a new insight in searching high mobility polar semiconductors, and point to BAs as a promising material for electronic and photovoltaic devices in addition to its predicted high thermal conductivity., Comment: 18 pages, 4 figures

We describe strategies to estimate the upper limits of the efficiency of photon energy harvesting via hot electron extraction from gapless absorbers. Gapless materials such as noble metals can be used for harvesting the whole solar spectrum, including visible and near-infrared light. The energy of photo-generated non-equilibrium or hot charge carriers can be harvested before they thermalize with the crystal lattice via the process of their internal photo-emission (IPE) through the rectifying Schottky junction with a semiconductor. However, the low efficiency and the high cost of noble metals necessitates the search for cheaper abundant alternative materials, and we show here that carbon can serve as a promising IPE material candidate. We compare the upper limits of performance of IPE photon energy-harvesting platforms, which incorporate either gold or carbon as the photoactive material where hot electrons are generated. Through a combination of density functional theory, joint electron density of states calculations, and Schottky diode efficiency modeling, we show that the material electron band structure imposes a strict upper limit on the achievable efficiency of the IPE devices. Our calculations reveal that graphite is a good material candidate for the IPE absorber for harvesting visible and near-infrared photons. Graphite electron density of states yields a sizeable population of hot electrons with energies high enough to be collected across the potential barrier. We also discuss the mechanisms that prevent the IPE device efficiency from reaching the upper limits imposed by their material electron band structures. The proposed approach is general and allows for efficient pre-screening of materials for their potential use in IPE energy converters and photodetectors within application-specific spectral windows., Comment: 17 pages, 6 figures

The phonon Boltzmann transport equation (BTE) has been widely utilized to study thermal transport in solids. While for a number of materials the exact solution to the BTE has been obtained for a uniform heat flow, problems arising in micro/nanoscale heat transport have been analyzed within the relaxation time approximation (RTA). Since the RTA breaks down at temperatures low compared to the Debye temperature, this approximation prevents the study of an important class of high Debye temperature materials such as diamond, graphite, graphene and some other 2D materials. We present a full scattering matrix formalism that goes beyond the RTA approximation and obtain a Green's function solution for the linearized BTE, which leads to an explicit expression for the phonon distribution and temperature field produced by an arbitrary spatio-temporal distribution of heat sources in an unbounded medium. The presented formalism is capable of describing a wide range of phenomena, from heat dissipation by nanoscale hot spots to the propagation of second sound waves. We provide numerical results for graphene for a spatially sinusoidal heating profile and discuss the importance of using the full scattering matrix compared to the RTA., Comment: 17 pages, 2 figures

In the hydrodynamic regime, phonons drift with a nonzero collective velocity under a temperature gradient, reminiscent of viscous gas and fluid flow. The study of hydrodynamic phonon transport has spanned over half a century but has been mostly limited to cryogenic temperatures (~1 K) and more recently to low-dimensional materials. Here, we identify graphite as a three-dimensional material that supports phonon hydrodynamics at significantly higher temperatures (~100 K) based on first-principles calculations. In particular, by solving the Boltzmann equation for phonon transport in graphite ribbons, we predict that phonon Poiseuille flow and Knudsen minimum can be experimentally observed above liquid nitrogen temperature. Further, we reveal the microscopic origin of these intriguing phenomena in terms of the dependence of the effective boundary scattering rate on momentum-conserving phonon-phonon scattering processes and the collective motion of phonons. The significant hydrodynamic nature of phonon transport in graphite is attributed to its strong intralayer sp2 hybrid bonding and weak van der Waals interlayer interactions. As a boundary-sensitive transport regime, phonon hydrodynamics opens up new possibilities for thermal management and energy conversion.

Last few years have witnessed significant enhancement of thermoelectric figure of merit of lead telluride (PbTe) via nanostructuring. Despite the experimental progress, current understanding of the electron transport in PbTe is based on either band structure calculation using first principles with constant relaxation time approximation or empirical models, both relying on adjustable parameters obtained by fitting experimental data. Here, we report parameter-free first-principles calculation of electron and phonon transport properties of PbTe, including mode-by-mode electron-phonon scattering analysis, leading to detailed information on electron mean free paths and the contributions of electrons and phonons with different mean free paths to thermoelectric transport properties in PbTe. Such information will help to rationalize the use and optimization of nanosctructures to achieve high thermoelectric figure of merit., Comment: 9 pages, 6 figures, 51 references

Generalized Ising models, also known as cluster expansions, are an important tool in many areas of condensed-matter physics and materials science, as they are often used in the study of lattice thermodynamics, solid-solid phase transitions, magnetic and thermal properties of solids, and fluid mechanics. However, the problem of finding the global ground state of generalized Ising model has remained unresolved, with only a limited number of results for simple systems known. We propose a method to efficiently find the periodic ground state of a generalized Ising model of arbitrary complexity by a new algorithm which we term cluster tree optimization. Importantly, we are able to show that even in the case of an aperiodic ground state, our algorithm produces a sequence of states with energy converging to the true ground state energy, with a provable bound on error. Compared to the current state-of-the-art polytope method, this algorithm eliminates the necessity of introducing an exponential number of variables to counter frustration, and thus significantly improves tractability. We believe that the cluster tree algorithm offers an intuitive and efficient approach to finding and proving ground states of generalized Ising Hamiltonians of arbitrary complexity, which will help validate assumptions regarding local vs. global optimality in lattice models, as well as offer insights into the low-energy behavior of highly frustrated systems.

Despite the long history of dislocation-phonon interaction studies, there are many problems that have not been fully resolved during this development. These include an incompatibility between a perturbative approach and the long-range nature of a dislocation, the relation between static and dynamic scattering, and the nature of dislocation-phonon resonance. Here by introducing a fully quantized dislocation field, the "dislon"[1], a phonon is renormalized as a quasi-phonon, with shifted quasi-phonon energy, and accompanied by a finite quasi-phonon lifetime that is reducible to classical results. A series of outstanding legacy issues including those above can be directly explained within this unified phonon renormalization approach. In particular, a renormalized phonon naturally resolves the decades-long debate between dynamic and static dislocation-phonon scattering approaches., Comment: 5 pages main text, 3 figures, 10 pages supplemental materials