Session-based recommendation (SBR) problem, which focuses on next-item prediction for anonymous users, has received increasingly more attention from researchers. Existing graph-based SBR methods all lack the ability to differentiate between sessions with the same last item, and suffer from severe popularity bias. Inspired by nowadays emerging contrastive learning methods, this paper presents a Simple Contrastive Graph Neural Network for Session-based Recommendation (SimCGNN). In SimCGNN, we first obtain normalized session embeddings on constructed session graphs. We...

We discuss thermodynamical stability for hairy black hole spacetimes, viewed as defects in the thermodynamical parameter space, taking into account the backreaction of a secondary hair onto the spacetime geometry, which is modified non trivially. We derive, in a model independent way, the conditions for the hairy black hole with the secondary hair to reach a stable thermal equilibrium with the heat bath. Specifically, if the scalar hair, induced by interactions of the matter fields...

The fractional differential equation $L^βu = f$ posed on a compact metric graph is considered, where $β>\frac14$ and $L = κ- \frac{\mathrm{d}}{\mathrm{d} x}(H\frac{\mathrm{d}}{\mathrm{d} x})$ is a second-order elliptic operator equipped with certain vertex conditions and sufficiently smooth and positive coefficients $κ,H$. We demonstrate the existence of a unique solution for a general class of vertex conditions and derive the regularity of the solution in the specific case of Kirchhoff vertex conditions. These results are extended...

Laser cooling of single atoms in optical tweezers is a prerequisite for neutral atom quantum computing and simulation. Resolved sideband cooling comprises a well-established method for efficient motional ground-state preparation, but typically requires careful cancellation of light shifts in so-called magic traps. Here, we study a novel laser cooling scheme which overcomes such constraints, and applies when the ground-state of a narrow cooling transition is trapped stronger than the excited state. We demonstrate our scheme,...

Let $k$ be an algebraically closed field of characteristic $p \geq 0$ and $V$ be a faithful $k$-rational representation of a finite $\ell$-group $G$, where $\ell$ is a prime number. The Noether problem asks whether $V/G$ is a stably rational variety. While if $\ell=p$ it is well-known that $V/G$ is always rational, when $\ell\neq p$, Saltman and then Bogomolov constructed $\ell$-groups for which $V/G$ is not stably rational. Hence, the geometry of $V/G$ depends heavily...

One of the central applications for quantum annealers is to find the solutions of Ising problems. Suitable Ising problems, however, need to be formulated such that they, on the one hand, respect the specific restrictions of the hardware and, on the other hand, represent the original problems which shall actually be solved. We evaluate sufficient requirements on such an embedded Ising problem analytically and transform them into a linear optimization problem. With an objective function...

Certifying the performance of quantum computers requires standardized tests. We propose a simple energy estimation benchmark that is motivated from quantum chemistry. With this benchmark we statistically characterize the noisy outcome of the IBM Quantum System One in Ehningen, Germany. We find that the benchmark results hardly correlate with the gate errors and readout errors reported for the device. In a time-resolved analysis, we monitor the device over several hours and find two-hour oscillations of...

In Monte Carlo simulations, proposed configurations are accepted or rejected according to an acceptance ratio, which depends on an underlying probability distribution and an a priori sampling probability. By carefully selecting the probability distribution from which random variates are sampled, simulations can be made more efficient, by virtue of an autocorrelation time reduction. In this paper, we illustrate how to directly sample random variates from a two dimensional truncated exponential distribution. We show that our...

Present-day Mars is cold and dry, but mineralogical and morphological evidence shows that liquid-water existed on the surface of ancient Mars. In order to explain this evidence and assess ancient Mars's habitability, one must understand the size and composition of the ancient atmosphere. Here we place constraints on the ancient Martian atmosphere by modeling the coupled, self-consistent evolution of atmospheric CO2, N2, and Ar on Mars from 3.8 billion years ago (Ga) to the present....

Correct prediction of the behavior of UO2 crystal, which is an antiferromagnet system with strongly-correlated electrons, is possible by using a modified density functional theory, the DFT+U method. In the context of DFT+U, the energy of crystal turns out to be a function with several local minima, the so-called meta-stable states, and the lowest energy state amongst them is identified as the ground state. OMC was a method that were used in DFT+U to determine...

Particle entanglement is a fundamental resource upon which are based many quantum technologies. However, the up-to-now best sources of entangled photons rely on parametric down-conversion processes, which are optimal only at certain frequencies, which rarely match the energies of condensed-matter systems that can benefit from entanglement. In this Letter, we show a way to circumvent this issue, and we introduce a new source of entangled photons based on resonance fluorescence delivering photon pairs as a...

Multiple Instance Learning (MIL) is a weakly supervised learning paradigm that is becoming increasingly popular because it requires less labeling effort than fully supervised methods. This is especially interesting for areas where the creation of large annotated datasets remains challenging, as in medicine. Although recent deep learning MIL approaches have obtained state-of-the-art results, they are fully deterministic and do not provide uncertainty estimations for the predictions. In this work, we introduce the Attention Gaussian Process...

Many tasks in video analysis and understanding boil down to the need for frame-based feature learning, aiming to encapsulate the relevant visual content so as to enable simpler and easier subsequent processing. While supervised strategies for this learning task can be envisioned, self and weakly-supervised alternatives are preferred due to the difficulties in getting labeled data. This paper introduces LRProp -- a novel weakly-supervised representation learning approach, with an emphasis on the application of temporal...

We establish strong mixing for the $\mathbb Z^d$-periodic, infinite horizon, Lorentz gas flow for continuous observables with compact support. The essential feature of this natural class of observables is that their support may contain points with infinite free flights. Dealing with such a class of functions is a serious challenge and there is no analogue of it in the finite horizon case. The mixing result for the aforementioned class of functions is obtained via new...

We show that a local non-Hermitian perturbation in a Hermitian lattice system generically induces scale-free localization for the continuous-spectrum eigenstates. Furthermore, when the local non-Hermitian perturbation enjoys parity-time (PT) symmetry, the PT symmetry breaking of continuous spectrum is always accompanied by the emergence of scale-free localization. This type of PT symmetry breaking is highly sensitive to boundary conditions: The continuous spectrum of a periodic system undergoes a PT symmetry breaking as long as the non-Hermitian...

Recent multi-modal contrastive learning models have demonstrated the ability to learn an embedding space suitable for building strong vision classifiers, by leveraging the rich information in large-scale image-caption datasets. Our work highlights a distinct advantage of this multi-modal embedding space: the ability to diagnose vision classifiers through natural language. The traditional process of diagnosing model behaviors in deployment settings involves labor-intensive data acquisition and annotation. Our proposed method can discover high-error data slices, identify influential...

We introduce a general method to engineer arbitrary Hamiltonians in the Floquet phase space of a periodically driven oscillator, based on the non-commutative Fourier transformation (NcFT) technique. We establish the relationship between an arbitrary target Floquet Hamiltonian in phase space and the periodic driving potential in real space. We obtain analytical expressions for the driving potentials in real space that can generate novel Hamiltonians in phase space, e.g., rotational lattices and sharp-boundary well. Our protocol...

We introduce classical and quantum no-signalling bicorrelations and characterise the different types thereof in terms of states on operator system tensor products, exhibiting connections with bistochastic operator matrices and with dilations of quantum magic squares. We define concurrent bicorrelations as a quantum input-output generalisation of bisynchronous correlations. We show that concurrent bicorrelations of quantum commuting type correspond to tracial states on the universal C*-algebra of the projective free unitary quantum group, showing that in the...

Oxygen-deficient layered perovskite YBaCuFeO$_{5}$ (YBCFO) is one rare type-II multiferroic material where ferroelectricity, driven by incommensurate spiral magnetic order, is believed to be achievable up to temperatures higher than room temperature. A cycloidal spiral rather than helical spiral order is essential ingredient for the existence of ferroelectricity in this material. Motivated by a recent experimental work on Mn-doped YBCFO where the spiral plane is observed to cant more towards the crystallographic $c$ axis upon Mn...

Let $\mathbb{k}$ be a characteristic zero domain. For a locally unital $\mathbb{k}$-superalgebra $A$ with distinguished idempotents $I$and even subalgebra $a \subseteq A_{\bar 0}$, we define and study an associated diagrammatic monoidal $\mathbb{k}$-linear supercategory $\mathbf{Web}^{A,a}_I$. This supercategory yields a diagrammatic description of the generalized Schur algebras $T^A_a(n,d)$. We also show there is an asymptotically faithful functor from $\mathbf{Web}^{A,a}_I$ to the monoidal supercategory of $\mathfrak{gl}_n(A)$-modules generated by symmetric powers of the natural module. When this functor is...

Spatiotemporal graph neural networks have shown to be effective in time series forecasting applications, achieving better performance than standard univariate predictors in several settings. These architectures take advantage of a graph structure and relational inductive biases to learn a single (global) inductive model to predict any number of the input time series, each associated with a graph node. Despite the gain achieved in computational and data efficiency w.r.t. fitting a set of local models, relying...

Anxiety levels in the AAVE community spiked in November 2022 as Avi Eisenberg performed an attack on AAVE. Eisenberg attempted to short the CRV token by using funds borrowed on the protocol to artificially deflate the value of CRV. While the attack was ultimately unsuccessful, it left the AAVE community scared and even raised question marks regarding the feasibility of large lending platforms under decentralized governance. In this work, we analyze Avi Eisenberg's actions and...

Energy efficient implementations and deployments of Spiking neural networks (SNNs) have been of great interest due to the possibility of developing artificial systems that can achieve the computational powers and energy efficiency of the biological brain. Efficient implementations of SNNs on modern digital hardware are also inspired by advances in machine learning and deep neural networks (DNNs). Two techniques widely employed in the efficient deployment of DNNs -- the quantization and pruning of parameters, can...

Recently, nonadiabatic geometric quantum computation has been received great attentions, due to its fast operation and intrinsic error resilience. However, compared with the corresponding dynamical gates, the robustness of implemented nonadiabatic geometric gates based on the conventional single-loop scheme still has the same order of magnitude due to the requirement of strict multi-segment geometric controls, and the inherent geometric fault-tolerance characteristic is not fully explored. Here, we present an effective geometric scheme combined with a...

Resistance distance has been studied extensively in the past years, with the majority of previous studies devoted to undirected networks, in spite of the fact that various realistic networks are directed. Although several generalizations of resistance distance on directed graphs have been proposed, they either have no physical interpretation or are not a metric. In this paper, we first extend the definition of resistance distance to strongly connected directed graphs based on random walks and...